Medical Image Processing is a growing application domain. Magnetic Resonance Imaging (MRI) may be used to provide a time-varying three dimensional image of the heart that can be used for diagnostic purposes. The cardiac images can be processed using general purpose computer vision techniques. However, these techniques fail to take fully advantage of the available prior knowledge from other domains such as physiology, cardiology, etc.
Cardiac segmentation is a well explored topic in Medical Image Analysis due to the fact that the outcome can have strong diagnostic power. Accuracy and precision are two important requirements in the segmentation of medical structures and, consequently, various boundary-driven methods have been developed for segmentation. These methods are based on the generation of a boundary image and the extraction of a continuous structure that accurately accounts for the boundary information.
For example, the well-known “snake” model is a pioneering framework that is the basis of significant boundary-driven image segmentation techniques (see, e.g., Kass, et al., “Snakes: Active Contour Models”, International Journal of Computer Vision, 1, pp. 321–332, 1988). Briefly, the snake model refers to an energy minimization technique that seeks the lowest potential of a curve-based objective function. This function is a compromise between a boundary image-driven attraction term and a term that accounts for the desired internal properties of the curve. According to the original snake model, the structure to be recovered refers to a set of points in the 2-D or 3-D space that is deformed locally towards the desired image characteristics while being constrained to respect some internal properties. Although this primitive approach has led to outstanding results, it can be sensitive to noisy or physically corrupted data.
Deformable templates and parameterized snakes such as B-splines and active shapes have been proposed on top of the original snake framework to overcome its poor performance on noisy data. Thus, prior to the segmentation process, a shape model is built using a certain number of training examples. This model refers to few parameters and can express a fairly large set of global and local deformations. The use of these methods can improve the segmentation performance under the condition that the general model can describe a fairly large portion of the eligible segmentation solutions. However, these models are quite sensitive to the initial conditions.
“Myopic” is a term often used to describe the dependency of the snake model from the initial conditions. The snake model is based on very local information and therefore the initial conditions have to be close enough from the optimal solution. Balloon forces have been proposed to liberate this model from the initial conditions. The central idea is to introduce a constant force that tends to continuously expand or shrink the initial structure. Clearly, this component can have a beneficial contribution to the original model under the condition that the initial structure either encircles the area to be recovered or is completely surrounded by the region to be segmented. This condition, however, cannot be easily met for general medical image segmentation applications.
In order to overcome these constraints, the use of regional/global information has been also considered and widely explored. The evolving contour is used to define an image partition that consists of two regions. The inner region refers to the area to be recovered and outer one to the rest of the image (background). Then, the global homogeneity regional properties are used to discriminate the region of interest from the background. These properties can be modeled using continuous probability density functions that are dynamically updated according to the latest segmentation map.
The evolution of boundary-based medical image segmentation techniques have led to a set of modules that deform an initial structure (set of points) towards the desired image characteristics. Based on these considerations, it is clear that the segmentation result will inevitably depend on the parameterization of the initial structure (position, number of the control points, etc.) Moreover, the technique that is used to re-parameterize the evolving structure will also hold a significant role in the segmentation process. Although various techniques have been proposed to deal with these issues, this dependency is not natural for an image segmentation approach.
Level Set Representations have been proposed as an alternative (to the Lagrangian) technique for evolving interfaces. These representations are a common choice for the implementation of variational frameworks in Computer Vision. The evolving contour is represented using a continuous zero-level set function of a higher dimension. Such representations can be implicit, intrinsic, parameter and topology free. The use of level set methods to evolve interfaces has led to an expansion of boundary-driven methods for image segmentation.
As is known in the art, the geodesic active contour refers to an optimization framework that was introduced as a geometric alternative to the original snake model. The main strength of this model is its implicit parameterization that can lead to a natural handling (through level sets) of topological changes (merging/splitting).
A step further, was the combination of boundary-driven flows with global regional intensity information and their implementation using the level set representations. The segmentation procedure then becomes quite independent from the initial conditions. Topological changes can be handled through the level set representations while arbitrary initial conditions can be dealt with by using global regional information. Such approaches are of great interest in medical image processing where structures are very complicated and consist of multiple components. However, they still suffer from robustness when noisy and incomplete data is to be dealt with. In addition, they fail to take advantage of the prior shape knowledge that is available from physiology regarding the medical structures to be segmented.
Some efforts have been made to address this limitation. For example, prior shape knowledge has been introduced to the geodesic active contour model. In another method, a shape influence term is combined with boundary and region-driven visual information to further increase the robustness of level set-based methods to noisy and incomplete data. One can claim that this objective can be met with the use of snakes and deformable templates.
Many medical applications involve the simultaneous extraction of multiple structures that are positioned in a constrained way (physiology) in the image plane. These high level (abstract) constraints can be transformed to low level segmentation modules according to the relative positions of the structures of interest. For example, one method for cortex segmentation considers a constrained (coupled) propagation of two contours according to some physical properties of the brain.
As noted above, Magnetic Resonance Imaging (MRI) provides time-varying three-dimensional imagery of the heart. To help in the diagnosis of disease, physicians are interested in identifying the heart chambers, the endocardium and the epicardium. Moreover measuring the ventricular blood volume, the ventricular wall mass, the ventricular wall motion and wall thickening properties over various stages of the cardiac cycle is a challenging task. The left ventricle is of particular interest because it pumps oxygenated blood from the heart to distant tissue in the entire body.
There have been methods proposed for cardiac segmentation. For example, Argus is a cardiac MR analysis package commercialized by Siemens with the MRease workstation attached to the magnetic resonance “MAGNETOM” systems. The system can perform the segmentation of 3D/4D data sets (volume slices varying in time) automatically. The segmentation algorithm comprises three different modules and is described in the reference by M. Jolly, “Combining Edge Region and Shape Information to Segment the Left Ventricle in Cardiac MR Images”, IEEE International Conference in Computer Vision, Vancouver, Canada, 2001. The automatic localization module is able to approximately locate the myocardium in a new image based on maximum discrimination. The system learned the gray level aspect of a heart (modeled as a Markov chain) by maximizing the Kullbach distance between the distributions of positive and negative examples of hearts. The local deformation process starts from an approximate contour and deforms it using Dijktra's shortest path algorithm. Multiple iterations of the algorithm are applied in a search space of increasing size around the proximate contour, therefore strengthening good edges and weakening faint edges. A graph cut algorithm is then used to finally choose the best edge pieces that are part of the endocardium. The epicardium is obtained by fitting a spline curve to the edge points outlined by Dijsktra's algorithm. Finally, the propagation module is responsible for providing an approximate starting point to the local deformations.